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Ferenc Kun and Zolt án Halász Department of Theoretical Physics University of Debrecen, Hungary

Crackling noise in fatigue fracture of heterogeneous materials. Ferenc Kun and Zolt án Halász Department of Theoretical Physics University of Debrecen, Hungary. J. S. Andrade Jr. and H. J. Herrmann Computational Physics, IfB, ETH, Z ü rich, Switzerland.

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Ferenc Kun and Zolt án Halász Department of Theoretical Physics University of Debrecen, Hungary

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  1. Crackling noise in fatigue fracture of heterogeneous materials Ferenc Kun and Zoltán Halász Department of Theoretical Physics University of Debrecen, Hungary J. S. Andrade Jr. and H. J. Herrmann Computational Physics, IfB, ETH, Zürich, Switzerland • Experiments: fatigue tests of heterogeneous materials • Theoretical approach: fiber bundle model for fatigue • Microscopic failure process: crackling noise 03/06/2008 UPoN 2008 Lyon, FranceCrackling Noise in Fatigue fracture

  2. Fatigue-life tests Experiments with asphalt Sub-critical periodic loading Fracture strength Disordered micro-structure • No instantaneous failure • Crack parallel to load • Accumulation of deformation • Complex time evolution • Number of cycles to break (lifetime) (Experiments by Jorge Soares, Univ. Fortaleza, Brasil) 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  3. Experimental results Evolution of deformation Basquin-law Power law Immediate breaking Increase of lifetime Origin of Basquin-law? Microscopic failure process? 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  4. Load parallel to fibers F • Perfectly brittle behaviour Two parameters: E, pth Distribution of failure thresholds E e LLS Fiber bundle model for fatigue • Discrete set of parallel fibers • on a regular lattice • Range of load redistribution GLS Two extremes: 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  5. Independent breaking thresholds • Breaking due to damage accumulation Joint distribution Nucleation rate of microcracks Dependence on loading history • Healing of damage limits the range of memory Microscopic failure mechanism Failure due to two physical mechanisms • Immediate response, breaking when 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  6. Equation of motion in GLS Integral equation: Damage accumulation and healing Static FBM deformation Initial condition: Parameters: Suppress damage Quasi-static limit: 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  7. Time evolution-constant load for various • monotonically increases • Finite lifetime • Larger smaller • Diverging derivative for Agreement with the experiments 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  8. Lifetime-number of cycles to break as a function of Lifetime Power law behavior where Independent of the type of disorder Basquin-law • Different disorder distributions • Different exponents 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  9. Loading at a constant Varying and Agreement with experiments fatigue limit Power law regime Rapid failure 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  10. Microscopic process of failure in GLS Low load value Red: immediate breaking Green: damage Long damage sequences Long waiting times Burst mainly at the end 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  11. Microscopic process of failure High load value Short damage sequences Short waiting times Strong bursting activity 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  12. Crackling noise in fatigue Fluctuations Separation of time scales Burst size Slow damage sequences Trigger immediate bursts Waiting time Bursts size Damage sequence Damage sequence Waiting time 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  13. Burst size distributions Universal power law behaviour Crossover for 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  14. Distributions-Scaling Waiting time Damage sequence Universal power laws 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  15. Localized load sharing • Load redistribution over • nearest intact neighbours • Stress concentration • Enhanced • Damage accumulation • Immediate breaking Bursts Growing clusters-cracks 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  16. Burst size distribution Power law distributions • for 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  17. Waiting time distributions Power law distributions Failure process gets faster • for Crossover to exponential 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  18. Cluster size distribution Growth and merging of clusters Power law behaviour 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

  19. Conclusions • Fiber bundle model of fatigue with GLS and LLS • Macro-scale • Reproduces Basquin law • Scaling law of deformation • Micro-scale • Crackling noise - bursts triggered by damage • Universalpower law distributions • Spatial and temporal correlations • Many open questions F. K., et al, J. Stat. Mech.:Theor. Exp. P02003 (2007). F. K., et al, Phys. Rev. Lett. 100, 094301 (2008). 03/06/2008 UPoN 2008 Lyon, France Crackling Noise in Fatigue Fracture

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